Can someone explain this?

Question

Linear and Quadratic Modeling Application Report

Selecting and Interpreting Your Model: In Weeks 3 and 4, you used the linear and quadratic models you created to forecast the food CPI for the next month. Include both forecasts in your report. Then, plot your forecast on the same graph as the data for each of the models. Use a visual inspection to decide which appears to best fit the general pattern of the data. Explain why you chose your model.

Writing the Report: Once you have decided on a model, write your report using the following format

Answer 1

Suppose you have been following food prices for several months and are trying to find a pattern.

One possibility is to use a "linear" model - for example, fitting a straight line to the price of bread as a function of time. If the line is rising, then the price of bread is rising, etc.

Another possibility is to use a quadratic model - instead of a straight line, fit a parabola to the data.

Each model will have a prediction for the next month, a month for which you don't yet have data.

So the problem here is to compare the two models. So first you plot the data, then you plot the line that "best fits" the data you have and the parabola that "best fits" the same data.

Which of the two curves is a better model? Decide and explain why you made the decision.

Some arguments are:
- all other things being equal, simple models are better, so if the line fits the data as well as the parabola, then we want to use the linear model.

- the fitting algorithm for one model may give too much weight to certain data points so the other model does a better job of reflecting the general trend

etc.